Hyperbolic 3-manifolds with Boundary Which are Side-pairings of Two Tetrahedra as Exteriors of Knotted Graphs in the 3-sphere

Authors

  • Juan Pablo Díaz Science Research Center, Institute for Research in Basic and Applied Sciences, Autonomous University of the State of Morelos (UAEM), Chamilpa, 62209 Cuernavaca, Mor., Mexico https://orcid.org/0000-0001-7831-3152
  • Gabriela Hinojosa Science Research Center, Institute for Research in Basic and Applied Sciences, Autonomous University of the State of Morelos (UAEM), Chamilpa, 62209 Cuernavaca, Mor., Mexico https://orcid.org/0000-0003-2916-4634

DOI:

https://doi.org/10.37256/cm.5220242910

Keywords:

3-manifolds with boundary, link complement, knotted graph

Abstract

In this paper, we give a generalization of Ivanšić’s method for hyperbolic 3-manifolds without boundary, which allows us to recognize if a hyperbolic 3-manifold with totally geodesic boundary, given by an isometric side-pairing of two hyperbolic truncated tetrahedra, is the exterior of a knotted graph; i.e., it is the complement of a 1-manifold with isolated singularities embedded in S3, in which case we get the corresponding diagram of the knotted isotopy class of its boundary. Otherwise, we obtain that the corresponding 3-manifold with boundary is the exterior of a knotted graph embedded in some lens space. Finally, we apply this method to a noncompact 3-manifold with a totally geodesic surface boundary of genus 2.

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Published

2024-04-26

How to Cite

1.
Díaz JP, Hinojosa G. Hyperbolic 3-manifolds with Boundary Which are Side-pairings of Two Tetrahedra as Exteriors of Knotted Graphs in the 3-sphere. Contemp. Math. [Internet]. 2024 Apr. 26 [cited 2024 May 28];5(2):1889-904. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/2910